Question: Solve for $x$ and $y$ using elimination. $\begin{align*}9x+2y &= 8 \\ 3x-2y &= 4\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $12x = 12$ Divide both sides by $12$ and reduce as necessary. $x = 1$ Substitute $1$ for $x$ in the top equation. $9( 1)+2y = 8$ $9+2y = 8$ $2y = -1$ $y = -\dfrac{1}{2}$ The solution is $\enspace x = 1, \enspace y = -\dfrac{1}{2}$.